What is the extreme f(x)=x^{5/3}-12x^{2/3} ?

The extreme f(x)=x^{5/3}-12x^{2/3} is Maximum(0,0),Minimum(24/5 ,-(144*3^{2/3})/(5*5^{2/3)})

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extreme f(x)=x^{5/3}-12x^{2/3}

extreme points

f (x) = x^{\frac{5}{3}} - 12 x^{\frac{2}{3}}

Maximum (0, 0), Minimum (\frac{24}{5}, - \frac{144 \cdot 3 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

Solution steps

f^{'} (x) = \frac{5 x - 24}{3 x ^{\frac{1}{3}}}

Find intervals:

Increasing

: - \infty < x < 0,

Decreasing

: 0 < x < \frac{24}{5},

Increasing

: \frac{24}{5} < x < \infty

Plug

x = 0

into

x^{\frac{5}{3}} - 12 x^{\frac{2}{3}} : 0

Maximum (0, 0)

Plug

x = \frac{24}{5}

into

x^{\frac{5}{3}} - 12 x^{\frac{2}{3}} : - \frac{144 \cdot 3 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}}

Minimum (\frac{24}{5}, - \frac{144 \cdot 3 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

Maximum (0, 0), Minimum (\frac{24}{5}, - \frac{144 \cdot 3 ^{\frac{2}{3}}}{5 \cdot 5 ^{\frac{2}{3}}})

What is the extreme f(x)=x^{5/3}-12x^{2/3} ?
The extreme f(x)=x^{5/3}-12x^{2/3} is Maximum(0,0),Minimum(24/5 ,-(144*3^{2/3})/(5*5^{2/3)})